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Publikacje
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[77860] Artykuł:

The use of differential geometry methods for linearization of nonlinear electrical circuits with multiple inputs and multiple outputs (MIMOs)

(Zastosowanie metod geometrii różniczkowej do linearyzacji nieliniowych obwodów elektrycznych posiadających wiele-wejść i wiele-wyjść (MIMOs).)
Czasopismo: ELECTRICAL ENGINEERING   Tom: 100, Zeszyt: 4, Strony: 2815-2824
ISSN:  0948-7921
Wydawca:  SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Opublikowano: Pażdziernik 2018
 
  Autorzy / Redaktorzy / Twórcy
Imię i nazwisko Wydział Katedra Do oświadczenia
nr 3
Grupa
przynależności
Dyscyplina
naukowa
Procent
udziału
Liczba
punktów
do oceny pracownika
Liczba
punktów wg
kryteriów ewaluacji
Sebastian Różowicz orcid logo WEAiIKatedra Elektrotechniki Przemysłowej i Automatyki**Takzaliczony do "N"Automatyka, elektronika, elektrotechnika i technologie kosmiczne507.50.00  
Andrzej Zawadzki orcid logo WEAiIKatedra Elektrotechniki Przemysłowej i Automatyki**Takzaliczony do "N"Automatyka, elektronika, elektrotechnika i technologie kosmiczne507.50.00  

Grupa MNiSW:  Publikacja w czasopismach wymienionych w wykazie ministra MNiSzW (część A)
Punkty MNiSW: 15
Klasyfikacja Web of Science: Article


Pełny tekstPełny tekst     DOI LogoDOI     Web of Science Logo Web of Science    
Słowa kluczowe:

Nieliniowy obwód MIMO  linearyzacja  transformacja przestrzeni stanów  linearyzacja sprzężeń  dyfeomorfizmy  Lie 


Keywords:

Nonlinear MIMO circuit  Linearization  State space transformation  Feedback linearization  Local diffeomorphism  Lie algebras 



Streszczenie:

W artykule przedstawiono przekształcenie nieliniowego obwodu elektrycznego MIMO w liniowy poprzez zmianę współrzędnych (lokalny dyfeomorfizm) z wykorzystaniem zamkniętej pętli sprzężenia zwrotnego. Podano niezbędne warunki, które muszą być spełnione przez nieliniowy system w celu umożliwienia linearyzacji procedur. Uwzględniono numeryczne rozwiązania równań stanu dla układu nieliniowego i równoważnego zlinearyzowanego układu.




Abstract:

The paper presents a transformation of nonlinear MIMO electrical circuit into linear one by a change of coordinates (local diffeomorphism) with the use of a closed feedback loop. The necessary conditions that must be fulfilled by a nonlinear system to make linearizing procedures possible are presented. Numerical solutions of state equations for the nonlinear system and equivalent linearized system are included.



B   I   B   L   I   O   G   R   A   F   I   A
[1] Gear W., “Numerical Initial Value Problems in Ordinary Differential Equations”, Prentice – Hall. Inc, 1971.
[2] Butcher J,C., “Numerical methods for Ordinary Differential Equations”, Wiley, 2003.
[3] Najm F.N., “Circuit Simulation”, John Wiley & Sons, Inc., Hoboken 2010.
[4] Brockett R.W., “Nonlinear systems and differential geometry”, Proc. Of IEEE, vol. 64, No.1, 1976, pp. 61–71.
[5] Brockett R. W., “Feedback invariants for nonlinear systems”, in Proc. 6th IFAC World Congr., Helsinki, Finland, vol. 6, 1978, pp. 1115–1120.
[6] Jakubczyk B. and Respondek W., “On linearization of control systems,” Bull. Acad. Polonaise, Sci., Ser., Sci., Math., vol. 28, 1980, pp. 517–522.
[7] Byrnes C. I. and Isidori A., “Local stabilization of minimum phase nonlinear systems”, Syst. Control Lett., vol. 11, 1988, pp. 9–19.
[8] Celikovsky S. and Nijmeijer H., “Equivalence of nonlinear systems to triangular form: the singular case”, Syst. Control Lett., vol. 27, 1996, pp. 135–144.
[9] Jakubczyk B., Respondek W., “On linearization of control systems,” Bull. Acad. Polonaise, Sci., Ser., Sci., Math., vol. 28, 1980, pp. 517–522.
[10] Isidori A., Krener A., Gori A. J., and Monaco S., “Nonlinear decoupling via feedback: A differential geometric approach,” IEEE Trans. Automat. Contr., vol. AC-26, 1981, pp. 331–345.
[11] Tall I.A., Respondek W., “Feedback Linearizable Strict Feedforward Systems”, in Proceedings of the 47th IEEE Conference on Decision and Control, Canc´un, Mexico, 2008, pp. 2499-2504,
[12] Isidori A., Nonlinear Control Systems: An Introduction, Springer, Berlin, 1989.
[13] Isidori A., Nonlinear Control Systems, Springer, Berlin, 1995.
[14] Nijmeijer H., van der Schaft A., Nonlinear Dynamical Control Systems, Springer-Verlag, New York 1991.
[15] Bodson M., Chiassons J., “Differential-geometric methods for control of electric motors”, International Journal of Circuit Theory and Applications, vol. 8, 1998, pp. 923-954.
[16] Su R., “On the linear equivalents of nonlinear systems,” Syst. Control Lett., vol. 2, 1982, pp. 48–52,
[17] Hunt L. R., Su R., and Meyer G., “Global transformations of nonlinear systems,” IEEE Trans. Automat. Contr., vol. AC-28, Jan. 1983, pp. 24–31.
[18] Fujimoto K., Sugie T., “Freedom in Coordinate Transformation for Exact Linearization and Its Application to Transient Behavior Improvement”, Automatica, vol. 37, 2001, pp. 137-144.
[19] Guay M., “Observer linearization of nonlinear systems by generalized tansformations”, Asian Journal of Control, vol. 7, no. 2, 2005, pp. 187-196.
[20] Jordan A. and Nowacki J.P., “Global linearization of non-linear state equations”, International Journal Applied Electromagnetics and Mechanics, vol. 19, 2004, pp. 637–642.
[21] Devanathan R.
Linearization Condition through State Feedback, IEEE Transactions on Automatic Control, Vol. 46, n. 8, 2001, pp. 1257-1260.
[22] Boukas T. K., Habetler T. G., High-Performance Induction Motor Speed Control Using Exact Feedback Linearization with State and State Derivative Feedback, IEEE Transactions on Power Electronics, 19, no. 4, 2004, pp. 1022-1028.
[23] Deutscher J., Schmid C., A state space embedding approach to approximate feedback linearization of single input nonlinear control systems, International Journal of Circuit Theory and Applications, 16, 2006, pp. 421–440.
[24] Wang D., Vidyasagar M., Control of a class of manipulators with the last link flexible – Part I: Feedback linearization, ASME Journal of Dynamic Systems, Measurement, and Control 113 (4) (1991) 655–661.
[25] Liu K.P.,. You W, Li Y.C., Combining a feedback linearization approach with input shaping for flexible manipulator control, International Conference on Machine Learning and Cybernetics 1, 2003, pp. 561–565.
[26] Jordan A., Kaczorek T., Myszkowski P., Linearization of nonlinear differential equations, Published by Bialystok University of Technology, Bialystok, 2007 (in Polish).
[27] Jordan A.J., “Linearization of non-linear state equation,” Bulletin of The Polish Academy of Sciences. Technical Sciences, vol. 54, no. 1, 2006, pp. 63-73.
[28] Elwakil A., Kennedy M., “Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices,” IEEE Transactions on Circuits and Systems-I, vol. 48 no.3, 2001, pp. 289-307.
[29] Zawadzki A., Różowicz S., “Application of input – state of the system transformation for linearization of some nonlinear generators,” International Journal of Control, Automation, and Systems, (accepted for publication: vol. 13, no. 3, 2015, pp.1-8.
[30] Zawadzki A., „Application of local coordinates rectification in linearization of selected parameters of dynamic nonlinear systems,” COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 33, no. 5, 2014, pp. 1819-1830.
[31] Seok Ho Jeon, Jin Young Choi, "Adaptive feedback linearization control based on stator fluxes modelfor induction motors ", Proceeding of the 15tIh International Symposium on Intelligent Control (ISIC 2000), July 2000, pp.273-278.
[32] Ouyang H., Wang J. and Huang L., "Robust output feedback stabilization for uncertain systems" IEE proc.-Control Theory Application, Vol.150, No. 5, September 2003.
[33] Sahjendra N. Singh, Meir Patcher," Adaptive feedback linearizing Nonlinear Close Formation Control of UA Vs " , Proceeding of the American Control Conference, June 2000, pp.854-858.
[34] Bourbaki N., Lie groups and Lie algebras Springer, Berlin, Chapters 1–3, (2002) Lie groups and Lie algebras Springer, Berlin, Chapters 4–6, 1998.
[35] Bump D., Lie Groups, Graduate Texts in Mathematics, Springer, New York, vol. 225, 2004.
[36] Serre J. P., Complex semisimple Lie algebras, Springer-Verlag, Berlin, 2001.